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Re: Problem



For the projectile, the speed squared as a function of time is:

V(t)^2 = (Vo*CosTH)^2 +(Vo*SinTH-gt)^2

Take the d/dt of this and see that this derivative goes to zero at the top
of the trajectory.

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Doug Craigen" <dcc@ESCAPE.CA>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, September 17, 2001 10:47 PM
Subject: Re: Problem


David Abineri wrote:

There is a question in Halliday/Resnick/Walker that I am using with my
high school class this year that bothers me and I wonder if someone
might help resolve it for me.

It shows a point object with a velocity vector pointing to the top of
the page and an acceleration vector pointing to the right side of the
page at a particular instant in time. It asks if the speed is
increasing
or decreasing?

It seems that one would have such a situation on a projectile at the
peak of its vertical motion (turning the page by 90 degrees) and then
its speed would be increasing.

On the other hand it could be an object on the left side of a circular
motion motion in which case the acceleration could the the centripetal
acceleration and the speed constant.

They say the speed is not changing.

Is the question in fact ambiguous?

Since the physical situation is not ambiguous, I can't see how the
answer would be. I'm pretty sure this describes uniform circular
motion, so I'll look at the other situation - a projectile at the top of
its
flight path. Yes the y-component of its velocity is changing and the
x-component is constant. As time progresses the velocity is vx*i -
9.8*t*j so the speed is (vx^2 + 9.8^2*t^2)^0.5. So differentiate this
wrt time and find its value at t=0... you will find the speed is
constant (= vx) at t=0.

This actually shows something else - what we tell the students in optics
- close the to center of a parabola the shape is approximates an arc.
At the top of its trajectory the projectile is momentarily undergoing
"circular motion".

\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\

Doug Craigen
http://www.dctech.com/physics/about_dc.html